{"title":"凯莱代数的高速率全秩空时分组码","authors":"T. Kiran, B. Sundar Rajan","doi":"10.1109/SPCOM.2004.1458506","DOIUrl":null,"url":null,"abstract":"For a quasi-static, multiple-input multiple-output (MIMO) Rayleigh fading channel, high-rate space-time block codes (STBCs) with full-diversity have been constructed in B. A. Sethuraman et al., (2003) for arbitrary number of transmit antennas, by using the regular matrix representation of an associative division algebra. While the 2/spl times/2 as well as 4/spl times/4 real-orthogonal design (ROD) V. Tarokh et al., (1999) and Alamouti code S. M. Alamouti (1998) were obtained as a special case of this construction, the 8/spl times/8 ROD could not be obtained. In this paper, starting with a non-associative division algebra (Cayley algebra or more popularly known as octonion algebra) over an arbitrary characteristic zero field F, a method of embedding this algebra into the ring of matrices over F is described, and high-rate full-rank STBCs for 8m (m, an arbitrary integer) antennas are obtained. We also give a closed form expression for the coding gain of these STBCs. This embedding when specialized to F=/spl Ropf/ and m=1, gives the 8/spl times/8 ROD.","PeriodicalId":424981,"journal":{"name":"2004 International Conference on Signal Processing and Communications, 2004. SPCOM '04.","volume":"56 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"High-rate full-rank space-time block codes from Cayley algebra\",\"authors\":\"T. Kiran, B. Sundar Rajan\",\"doi\":\"10.1109/SPCOM.2004.1458506\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a quasi-static, multiple-input multiple-output (MIMO) Rayleigh fading channel, high-rate space-time block codes (STBCs) with full-diversity have been constructed in B. A. Sethuraman et al., (2003) for arbitrary number of transmit antennas, by using the regular matrix representation of an associative division algebra. While the 2/spl times/2 as well as 4/spl times/4 real-orthogonal design (ROD) V. Tarokh et al., (1999) and Alamouti code S. M. Alamouti (1998) were obtained as a special case of this construction, the 8/spl times/8 ROD could not be obtained. In this paper, starting with a non-associative division algebra (Cayley algebra or more popularly known as octonion algebra) over an arbitrary characteristic zero field F, a method of embedding this algebra into the ring of matrices over F is described, and high-rate full-rank STBCs for 8m (m, an arbitrary integer) antennas are obtained. We also give a closed form expression for the coding gain of these STBCs. This embedding when specialized to F=/spl Ropf/ and m=1, gives the 8/spl times/8 ROD.\",\"PeriodicalId\":424981,\"journal\":{\"name\":\"2004 International Conference on Signal Processing and Communications, 2004. SPCOM '04.\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2004 International Conference on Signal Processing and Communications, 2004. SPCOM '04.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SPCOM.2004.1458506\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2004 International Conference on Signal Processing and Communications, 2004. SPCOM '04.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SPCOM.2004.1458506","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
对于准静态、多输入多输出(MIMO)瑞利衰落信道,B. a. Sethuraman等人(2003)通过使用关联除代数的正则矩阵表示,为任意数量的发射天线构建了具有全分集的高速率空时分组码(stbc)。虽然V. Tarokh等人(1999)和Alamouti规范S. M. Alamouti(1998)作为这种结构的特例获得了2/spl倍/2和4/spl倍/4实正交设计(ROD),但无法获得8/spl倍/8的ROD。本文从任意特征零域F上的非结合除法代数(Cayley代数或更普遍地称为八元代数)开始,描述了将该代数嵌入到F上的矩阵环中的方法,并获得了8m (m,任意整数)天线的高速率全秩stbc。我们还给出了这些stbc的编码增益的封闭表达式。这种嵌入在F=/spl Ropf/和m=1时,得到8/spl times/8 ROD。
High-rate full-rank space-time block codes from Cayley algebra
For a quasi-static, multiple-input multiple-output (MIMO) Rayleigh fading channel, high-rate space-time block codes (STBCs) with full-diversity have been constructed in B. A. Sethuraman et al., (2003) for arbitrary number of transmit antennas, by using the regular matrix representation of an associative division algebra. While the 2/spl times/2 as well as 4/spl times/4 real-orthogonal design (ROD) V. Tarokh et al., (1999) and Alamouti code S. M. Alamouti (1998) were obtained as a special case of this construction, the 8/spl times/8 ROD could not be obtained. In this paper, starting with a non-associative division algebra (Cayley algebra or more popularly known as octonion algebra) over an arbitrary characteristic zero field F, a method of embedding this algebra into the ring of matrices over F is described, and high-rate full-rank STBCs for 8m (m, an arbitrary integer) antennas are obtained. We also give a closed form expression for the coding gain of these STBCs. This embedding when specialized to F=/spl Ropf/ and m=1, gives the 8/spl times/8 ROD.